# Theoretical Physics

### A Method to Evaluate Quantum Path Integrals

Download PDF (473.1 KB) PP. 7 - 13 Pub. Date: March 21, 2017

### Author(s)

**Babak Vakili**^{*}

Department of Basic Sciences, Tonekabon Branch, Islamic Azad University (IAU), Tonekabon, Iran

### Abstract

As an alternative formulation of quantum mechanics, path integral is based on the
notion of transition amplitude which gives the wave function of a quantum system at a time

*t*by acting on the wave function at an earlier time_{f}*t*. We show that for a general quadratic form for the Lagrangian of the system, transition amplitude has the form f(_{i}*t*−_{f}*t*)e_{i}^{i/hSclass}. , where*Sclass*. is the classical action. We then present an algebraic method to evaluate the function*f*(*t*−_{f}*t*) without refereing to the path integral calculations. We examine the presented method to the cases of free particle and harmonic oscillator and obtain their propagators._{i}### Keywords

Path integral, classical action.

### References

[1] R.P. Feynman and A.R. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill, New York, 1965.

[2] P.A.M. Dirac, The Principles of Quantum Mechanics, Oxford University Press, 1958. P.A.M. Dirac, Lectures on Quantum Mechanics, Dover Publications, New York, 1964.

[3] A. Das, Field theory, a path integral approach, Word Scientific Publishing, Singapore, 1993.

[4] R. Shankar, Principles of Quantum Mechanics, Plenum Press, New York, 1994.